Method and apparatus for I/Q mismatch calibration in a receiver

ABSTRACT

A method for I/Q mismatch calibration of a receiver having an I/Q correction module with correction parameters, comprising the steps of generating a test signal containing a single tone waveform with frequency of a carrier frequency plus a predetermined frequency, applying I/Q demodulation to reduce the central frequency of the test signal and outputting a demodulated signal, converting the demodulated signal to a digital signal, obtaining measures of the digital signal respectively indicative of the frequency response of the digital signal at the plus and minus predetermined frequencies, and calculating the set of the correction parameters for the I/Q correction module based on the measures.

FIELD OF THE INVENTION

The present invention relates to compensation of physical layerimpairments in communication systems and particularly to a method andapparatus for I/Q mismatch calibration in a receiver.

DESCRIPTION OF THE PRIOR ART

OFDM is a multi-channel modulation system employing Frequency DivisionMultiplexing (FDM) of orthogonal sub-carriers, each modulating a lowbit-rate digital stream. The simplest way to describe an orthogonalfrequency-division multiplexing (OFDM) signal is as a set of closelyspaced frequency-division multiplexed carriers. While this is a goodstarting point for those unfamiliar with the technology, it falls shortas a model for analyzing the effects of signal impairment.

The reason it falls short is that the carriers are more than closelyspaced; they are heavily overlapped. In a perfect OFDM signal, theorthogonality property prevents interference between overlappingcarriers. This is different from the FDM systems. In FDM systems, anyoverlap in the spectrums of adjacent signals will result ininterference. In OFDM systems, the carriers will interfere with eachother only if there is a loss of orthogonality. So long as orthogonalitycan be maintained, the carriers can be heavily overlapped, allowingincreased spectral efficiency.

Table 1 lists a variety of common analog signal impairments and theireffects on both OFDM signals and the more familiar single-carriermodulations such as quadrature phase-shift keying (QPSK) or 64-QAM(quadrature amplitude modulation). Most of these impairments can occurin either the transmitter or the receiver.

Impairment OFDM QPSK I/Q gain balance State spreading Distortion of(uniform/carrier) constellation I/Q quadrature State spreadingDistortion of skew (uniform/carrier) constellation I/Q channel Statespreading State spreading mismatch (non-uniform/ carrier) UncompensatedState spreading Spinning frequency error constellation Phase noise Statespreading Constellation (uniform/carrier) phase arcing Nonlinear Statespreading State spreading distortion Linear distortion Usually no effectState spreading (equalized) if not equalized Carrier leakage Offsetconstellation Offset constellation for center carrier only (if used)Frequency error State spreading Constellation phase arcing Amplifierdroop Radial constellation Radial constellation distortion distortionSpurious State spreading or State spreading, shifting of affectedgenerally circular sub-carrier

For cost reasons, analog in-phase and quadrature (I/Q) modulators anddemodulators are often used in transceivers—especially for widebandwidth signals. Being analog, these I/Q modulators and demodulatorsusually have imperfections that result in an imperfect match between thetwo baseband analog signals, I and Q, which represent the complexcarrier. For example, gain mismatch might cause the I signal to beslightly different from the Q. In a single-carrier modulation system,this results in a visible distortion in the constellation—the squareconstellation of a 64-QAM signal would become rectangular.

To better understand how gain imbalance will affect an OFDM signal, lookat the equations describing each individual sub-carrier. In thefollowing analysis, it is important to keep in mind that, while anindividual sub-carrier is analyzed, the I/Q gain imbalance error is onthe signal that is the composite of all sub-carriers.

In the equation (1), C_(k,m) is a complex number representing thelocation of the symbol within the constellation for the kth sub-carrierat the mth symbol time. For example, if sub-carrier k isbinary-phase-shift-keying (BPSK) modulated, then C_(k,m) might take onvalues of ±1+j0. The complex exponential portion of equation (1)represents the kth sub-carrier, which is amplitude- and phase-modulatedby the symbol C_(k,m). Therefore:C_(k,m)(e^(j2πkΔft))  (1)

Using Euler's relation, the equation (1) can be rewritten as:C_(k,m)(cos(2π·kΔft)+j sin(2π·kΔft))  (2)

Now add the term “β” to represent gain imbalance. For a perfect signal,set β=0. As shown, the gain imbalance term will also produce a gainchange. This was done to simplify the analysis. Therefore:C_(k,m)((1+β) cos(2π·kΔft)+j sin(2π·kΔft)  (3)

The equation can be rearranged and this can be rewritten as the sum of aperfect signal and an error signal:C_(k,m)(cos(2π·kΔft)+j sin(2π·kΔft))+C_(k,m)β cos(2π·kΔft)  (4)

Finally, converting back into complex exponential notation, we get:

$\begin{matrix}{{C_{k,m}{\mathbb{e}}^{{j2\pi}\; k\;{\Delta{ft}}}} + {\left( {C_{k,m}\frac{\beta}{2}} \right) \cdot \left( {{\mathbb{e}}^{{j2\pi}\; k\;{\Delta{ft}}} + {\mathbb{e}}^{{- {j2\pi}}\; k\;{\Delta{ft}}}} \right)}} & (5)\end{matrix}$

In words, the equation (5) shows that a gain imbalance produces twoerror terms. The first error term is at the frequency of the kthsub-carrier. The second error term is at the frequency of the −kthsub-carrier. The phase and magnitude of the error terms are proportionalto the symbol received on the kth sub-carrier. Another way of sayingthis is that I/Q gain imbalance will result in each sub-carrier beinginterfered with by its frequency mirror-image sub-carrier. Personsskilled in the art will instantly recognize this as imperfect sidebandcancellation.

The equation (5) has several implications. First, it is generally truethat for sub-carriers used to carry data (as opposed to pilots), thesymbol received at any given time on the kth sub-carrier is uncorrelatedto the symbol on the −kth sub-carrier.

For a given sub-carrier, the lack of correlation from the mirror-imagesub-carrier implies a certain randomness to the error. This results in aspreading of the sub-carrier's constellation states in a noise-likefashion. This is especially true for higher-order modulations such as64-QAM. For lower-order modulations, such as BPSK, the error term fromthe mirror-image carrier has fewer states.

This can result in constellations where the BPSK pilot carriers of an802.11a signal exhibit spreading that does not appear noise-like. Also,as the BPSK pilots do not have an imaginary component; the error termsassociated with the pilot sub-carriers are real—so the spreading is onlyalong the real (I) axis. Note that the phase relationships between thepilot carriers in an 802.11a system are highly correlated, so the errorsintroduced by quadrature errors are not random.

Quadrature skew produces error terms similar to those produced by gainimbalance. Quadrature skew occurs when the two oscillators used in anI/Q modulator or demodulator do not differ by exactly 90°. For a smallangular error, it can be shown that the resulting error is orthogonal tothe data. This is indicated by the j in front of the error terms in theequation (6). As with gain imbalance, the error generates energy at thekth and −kth sub-carriers. Again, the 802.11a BPSK pilots do not have animaginary component, so the error term, which is now orthogonal, causesspreading along the Q axis. For the QPSK carriers in this example, theerror is also orthogonal. However, unlike BPSK, a QPSK constellationdoesn't look any different when rotated by 90°. (See the equation (6).):

$\begin{matrix}{{C_{k,m}{\mathbb{e}}^{{j2\pi}\; k\;{\Delta{ft}}}} + {j{\frac{C_{k,m}\phi}{2} \cdot \left( {{\mathbb{e}}^{{j2\pi}\; k\;{\Delta{ft}}} + {\mathbb{e}}^{{- {j2\pi}}\; k\;{\Delta{ft}}}} \right)}}} & (6)\end{matrix}$

In both 802.11a and Hiperlan2, a channel estimation sequence istransmitted at the beginning of a burst. This special sequence is usedto train the receiver's equalizer. The intended function of theequalizer is to compensate the received signal for multi-pathdistortion—a linear impairment in the signal that is the result ofmultiple signal paths between the transmitter and the receiver. As theideal channel estimation sequence is known by the receiver, the receivercan observe the effects of the channel on the transmitted signal andcompute a set of equalizer coefficients.

In the transmitter, the channel estimation sequence is created by BPSKmodulating all 52 carriers for a portion of the preamble. Notcoincidentally, the equalizer consists of 52 complex coefficients—onefor each sub-carrier. It should come as no surprise that eachsub-carrier in the channel estimation sequence has the greatestinfluence on the equalizer coefficient computed for that samesub-carrier.

The channel estimation sequence, and the receiver algorithms thatcompute the equalizer coefficients, are not immune from signalimpairments. Consider, for example, the effect of I/Q gain imbalance onsub-carriers +26 and −26 of the channel estimation sequence. Recall fromequation (5) that each sub-carrier has two error terms: one at the samefrequency as the sub-carrier, and one at the mirror image frequency. TheI/Q gain imbalance will cause mutual interference between sub-carriers+26 and −26.

From the IEEE 802.11a standard, the sub-carrier modulation for thechannel estimation sequence is defined to be C⁻²⁶=1+j0 and C₊₂₆=1+j0.Using these values in equation (5), one can easily determine that thetwo sub-carriers, when combined with the resulting error terms, willsuffer an increase in amplitude. The equalizer algorithm will be unableto differentiate the error from the actual channel response, and willinterpret this as a channel with too much gain at these two sub-carrierfrequencies. The equalizer will incorrectly attempt to compensate byreducing the gain on these sub-carriers for subsequent data symbols.

The result will be different for other sub-carrier pairs, depending onthe BPSK channel estimation symbols assigned to each.

With QPSK sub-carriers, the equalizer error caused by gain imbalance, orquadrature skew, results in seven groupings in each corner. Each QPSKsub-carrier suffers from QPSK interference from its mirror image. Thisresults in a spreading to four constellation points in each corner. EachQPSK sub-carrier also suffers from a bi-level gain error introduced bythe equalizer. This would produce eight groupings, except that the gainerror is such that corners of the groupings overlap at the ideal cornerstate. Only seven groupings are visible.

I/Q Channel Mismatch

When the frequency response of the baseband I and Q channel signal pathsare different, an I/Q channel mismatch exists. I/Q channel mismatch canbe modeled as a sub-carrier-dependent gain imbalance and quadratureskew. I/Q gain imbalance and quadrature skew, as described above, aresimply a degenerate form of I/Q channel mismatch in which the mismatchis constant over all sub-carriers. Think of channel mismatch as gainimbalance and quadrature skew as a function of a sub-carrier. It isstill generally true that channel mismatch causes interaction betweenthe kth and −kth sub-carriers, but that the magnitude of the impairmentcould differ between the kth and the (k+n) th carriers.

In order to eliminate the effects of the previously describedimpairments on the OFDM systems, various kinds of compensation circuitsand methods have been proposed.

FIG. 1 shows the quadrature gain and phase imbalance correctioncircuitry of a receiver disclosed in U.S. patent application Ser. No.285151. FIG. 1 illustrates a communications device 110 suitable forreceiving and correcting I and Q (In phase and Quadrature phase)signals. There are two essential parts to the device 110, the path ofthe received signals and the signal path of the signals used to mix withthe received signals. The received signal path includes a low noiseamplifier 111, two mixers 112 and 113, two coupling capacitors 114 and115 and two filters 116 and 117. Finally the signal path contains gainamplifiers 118 and 119 before the received signal is input into A/Dconverters 120 and 121 for processing by the digital signal processor122. The mixing signals are produced using local oscillators 123 and124, a phase locked loop 125, a filter 126, a phase shifter 127 and amixer 128.

In the received signal path, the LNA (111) is a standard low noiseamplifier commonly used to amplify low power high frequency RF signals.The incoming radio signal LNA comes from an antenna (not shown). Thereceived signal will be broken into quadrature components by usingmixing circuits M1 (112) and M2 (113) and phase adjusting circuit P1(129). The outputs of M1 and M2 will become the baseband signals. As isconventional in quadrature circuits, capacitors C1 and C2 (114 and 115)are used to block any DC components of the received signal and filtersF1 and F2 (116 and 117) are used to further filter unwanted signals.Before any I/Q modulation is performed however, it is critical that thereceiver be properly calibrated.

In order to produce a reliable calibration tone in the mixing signalpath, the local oscillator L1 (123) is mixed with a low frequency toneproduced by L2 (124). An example of these frequencies would be L1 set at5 Gigahertz, while L2 is set at 5 Megahertz. The local oscillator L1 isalso used with a Phase Locked Loop PLL (125) and a filter F3 (126).These two signals are multiplied by a mixing circuit M4 (128). Theresulting multiplication of two sine waves of differing frequenciesresults in two signals being produced, wherein the resulting sine waveare at different frequencies. Therefore the mixer M4 produces twosignals for the calibration process.

The two calibration tones will be fed into Mixers M1 and M2 forquadrature processing. The In-phase branch would be a clear signal butthe Quadrature phase would be zero. In order to overcome this problem, aPhase Shifter P2 is implemented. The phase shifter P2 adds an angletheta to the frequency of a calibration tone signal. For example, whenP2 is set to zero, V_(I)(t) is cos (ωt) and V_(Q)(t) is zero. When P2 isset to 90 degrees, the V_(I)(t) signal is nonexistent while V_(Q)(t) iscos (ωt).

The calibration process using Phase Shifter P2 (127) would then be asfollows. P2 is adjusted so as to obtain the maximum value of signal inthe V_(I)(t) branch. The adjustment of P2 is performed by the DigitalSignal Processing chip (122). The maximum signal level is measured bybaseband processor chip 122 and stored. Then P2 is adjusted by 90degrees until the signal in the Q branch is at a maximum level. Themaximum level of the Q branch is also measured and stored in thebaseband processor chip 122. Once these maximum values of each branchare known, the baseband processor chip may perform a gain imbalancecalibration. This gain imbalance correction may be performed byamplifiers G1 and G2 (118 and 119) or after analogue to digital signalconversion (A/D) in the baseband processor chip 122. It is noted that G1and G2 may perform the gain adjustments for the receiver as a whole. Itis also noted that G1 and G2 are controlled together as opposed toseparately. The I and Q gains are therefore made equal to avoid anysideband production and distortion of the desired signal. The presentinvention also allows for gain imbalance calibration to be performed atany level of gain as set by G1 and G2.

With respect to the I/Q phase error calibration, P2 would be set at anangle such as 45 degrees. This ensures a signal of almost equal value inboth the I and Q branches. By simply multiplying the two signals one candetect the relative phase of the I and Q branches. The product of a sineand cosine signal should result in zero. Mixer circuit M3 (131)accomplishes the multiplication of the I and Q signals and outputs asignal to the filter F4 (130). If this is not the case, meaning that theI and Q branches are not exactly 90 degrees out of phase as desired, aphase error signal is produced. This signal is fed back through anamplifier and filter EF to Phase Shifter P1 to compensate for the error.Ideally the phase difference between the I and Q branches should be 90degrees. Therefore, the adjustment of P2 with the appropriate gaincontrol in addition with the adjustment of P1, allow for an optimumphase imbalance to be achieved. It is noted that P1 may be in the RFpath instead of being in the local oscillator path if desired.

U.S. Pat. No. 6,122,325 also discloses a method for detecting andcorrecting in-phase/quadrature imbalance in digital communicationreceivers. The method includes the steps of assuming that a signalimbalance exists in the received signal, the signal imbalance having anamplitude imbalance and a phase imbalance, generating an amplitudeimbalance correction factor and a phase imbalance correction factor tolessen the signal imbalance, and re-evaluating the amplitude and phaseimbalance correction factors over a set of readings of the in-phase andquadrature components until the signal imbalance is minimized.

U.S. Pat. No. 5,949,821 discloses an apparatus for correcting phase andgain imbalance between in-phase and quadrature components of a receivedsignal based on a determination of peak amplitudes. As shown in FIG. 2,it includes an equalizer 226 for correcting imbalance between in-phaseand quadrature components of a received signal. The equalizer 226determines peak amplitude for the in-phase and quadrature components,and the phase imbalance between both components. At least one of thein-phase and quadrature components is adjusted based on a function ofthe phase imbalance, and of the ratio of peak amplitudes of the in-phaseand quadrature components.

Although there are already many kinds of compensation circuits andmethods, it is still a goal of research to propose newer and bettersolutions to the I/Q mismatch problems in a receiver.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a new method andapparatus for I/Q mismatch calibration of a receiver.

To achieve the above-mentioned object, the present invention provides amethod for I/Q mismatch calibration of a receiver having an I/Qcorrection module with correction parameters A_(p) and B_(p), comprisingthe steps of generating a test signal containing a single tone waveformwith frequency of a carrier frequency f_(c) Hz plus a predeterminedfrequency f_(T) Hz, applying I/Q demodulation to reduce the centralfrequency of the test signal by f_(c) Hz and outputting a demodulatedsignal, converting the demodulated signal to a digital signal, obtainingmeasures U₁ and U₂ of the digital signal where U₁ and U₂ are valuesindicative of the frequency response of the digital signal at frequency+f_(T) Hz and −f_(T) Hz, respectively, and calculating the set of thecorrection parameters A_(p) and B_(p) for the I/Q correction modulebased on the measures U₁ and U₂.

In addition, the present invention provides an apparatus for I/Qmismatch calibration of a receiver having an I/Q correction module withcorrection parameters A_(p) and B_(p). A signal generator generates atest signal containing a single tone waveform with frequency of acarrier frequency f_(c) Hz plus a predetermined frequency f_(T) Hz. Ademodulator applies I/Q demodulation to reduce the central frequency ofthe test signal by f_(c) Hz and outputs a demodulated signal. An A/Dconverter converts the demodulated signal to a digital signal. Adual-tone correlator obtains measures U₁ and U₂ of the digital signalwhere U₁ and U₂ are values indicative of the frequency response of thedemodulated signal at frequency +f_(T) Hz and −f_(T) Hz, respectively. Aprocessor obtains the set of the correction parameters A_(p) and B_(p)according to the measures U₁ and U₂.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawings,given by way of illustration only and thus not intended to be limitativeof the present invention.

FIG. 1 shows a quadrature gain and phase imbalance correction circuitryof a receiver disclosed in U.S. patent application Ser. No. 285151.

FIG. 2 shows an apparatus for correcting phase and gain imbalancebetween in-phase and quadrature components of a received signal based ona determination of peak amplitudes disclosed in U.S. Pat. No. 5,949,821.

FIG. 3 shows a setup of RX I/Q channel mismatch calibration for 802.11gof a receiver according to the embodiment of the present invention.

FIG. 4 is a flowchart of a method for I/Q mismatch calibration of areceiver according to the embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The mathematical theories of the invention will be described in thefollowing.

The equivalent baseband signals for the I and Q channels before the I/Qdemodulation are represented as x_(I)(t) and x_(Q)(t) respectively.Ideally, the signal before the I/Q demodulation can be expressed as

$\begin{matrix}\begin{matrix}{{r(t)} = {{{x_{I}(t)} \cdot {\cos\left( {2\pi\; f_{c}t} \right)}} - {{x_{Q}(t)} \cdot {\sin\left( {2\pi\; f_{c}t} \right)}}}} \\{= {{Re}\left\{ {{x(t)} \cdot {\mathbb{e}}^{{j2\pi}\; f_{c}t}} \right\}}}\end{matrix} & (7)\end{matrix}$where x(t)=X_(I)(t)+jx_(Q)(t) and f_(c) denotes the carrier frequency.Assuming that an amplitude mismatch a and a phase mismatch θ resultsfrom the I/Q demodulation, the baseband signals y_(I)(t) and y_(Q)(t)for the I and Q channels after the I/Q demodulation are, without loss ofgenerality, given by the equations:y ₁(t)=x _(I)(t)·(1+α)·cos(θ/2)+x _(Q)(t)·(1+α)·sin(θ/2)  (8)y _(Q)(t)=x _(I)(t)·(1−α)·sin(θ/2)+x _(Q)(t)·(1−α)·cos(θ/2)

The combined baseband signal y(t) after the I/Q demodulation can beexpressed as y_(I)(t)+jy_(Q)(t). Thus, from the equation (8), thefollowing equation can be derived:y(t)=A·x(t)+B·x*(t)  (9)where A and B are complex numbers with

$\begin{matrix}{{A = {\frac{1}{2}\left\{ {{\left( {1 + \alpha} \right){\mathbb{e}}^{{j\theta}/2}} + {\left( {1 - \alpha} \right){\mathbb{e}}^{{- {j\theta}}/2}}} \right\}}}{B = {\frac{1}{2}\left\{ {{\left( {1 + \alpha} \right){\mathbb{e}}^{{j\theta}/2}} - {\left( {1 - \alpha} \right){\mathbb{e}}^{{- {j\theta}}/2}}} \right\}}}} & (10)\end{matrix}$

For receiver I/Q mismatch compensation, we may compensate the signalafter the A/D conversion. Two A/D convertors are needed. The first A/Dconvertor is used for converting the I channel signal y_(I)(t) to a Ichannel digital signal Y_(I)[n], while the second A/D convertor is usedfor converting the Q channel signal y_(Q)(t) to a Q channel digitalsignal y_(Q)[n]. Let y[n]=y_(I)[n]+jy_(Q)[n] denote the sampled signalof y(t) and w[n]=D(y[n]) be the compensated output. The compensationequation may bew[n]=A _(p) y[n]+B _(p) y*[n]  (11)Ideally, after the compensation, w[n]=C·x[n] where C is a constant. Bysubstituting y[n]=A·x[n]+B·x*[n] into the equation (11), we derive:w[n]=(A _(p) ·A+B _(p) ·B*)·x[n]+(A _(p) ·B+B _(p) ·A*)·x*[n]  (12)Accordingly, the equation w[n]=C·x[n] is satisfied only if

$\begin{matrix}\left\{ \begin{matrix}{{{A_{p} \cdot B} + {B_{p} \cdot A^{*}}} = 0} \\{{{A_{p} \cdot A} + {B_{p} \cdot B^{*}}} = C}\end{matrix} \right. & (13)\end{matrix}$Therefore, the goal of the calibration method in the invention is theidentification of the coefficients A_(p) and B_(p) which satisfyequation (13).

The I/Q mismatch should be measured over the pass band frequency range(e.g., over 0 to 8 MHz for the case of 802.11 g). We consider theestimation of the gain mismatch over a specific frequency of f_(T) Hz,i.e., 2.5 MHz, for the 802.11a OFDM system. Note that, in general, f_(T)could be a positive or negative real number. Let f_(c) be the carrierfrequency. A single-tone test signal is generated at frequencyf_(c)+f_(T).

FIG. 3 shows a setup of RX I/Q channel mismatch calibration for 802.11gof a receiver according to the embodiment of the present invention. Asignal generator 30 generates a test signal x(t) which contains asingle-tone waveform which can be expressed as cos(2π(f_(c)+f_(T))t).The frequency and the power of the single-tone waveform are under thecontrol of a personal computer 31. This waveform is fed into the DUT(device under test) 32. The RF section 321 of the DUT 32 down-convertsthe test signal x(t) to a baseband signal x_(dem)(t). To speak morespecifically, the RF section 321 of the DUT 32 demodulates the testsignal x(t) by reducing the central frequency of the test siganl x(t) byf_(c) Hz and outputting a demodulated signal x_(dem)(t). This basebandsignal x_(dem)(t) is sampled by the analog-to-digital converters (ADC)322 with a sampling rate of, for example, 40 MHz and is converted to adigital signal x_(dem)[n]. Note that two ADCs are needed. The first ADCis used for converting the real part of x_(dem)(t) to a real part ofdigital signal x_(dem)[n], while the second ADC is used for convertingthe imaginary part of signal x_(dem)(t) to the imaginary part of digitalsignal x_(dem)[n]. The I/Q correction module 33 corrects the I/Qmismatch in the signal outputted from the ADC 322 by a functionw[n]=A_(p)·x_(dem)[n]+B_(p)·x*_(dem)[n], where w[n] is the correctedsignal, x_(dem)[n] is the signal from the ADC 322, and A_(p) and B_(p)are correction coefficients. In the purposed I/Q calibration stage, thecorrecting coefficients A_(p) and B_(p) are initially set to A_(p)=1 andB_(p)=0. In other words, the I/Q correction module is transparent in theI/Q calibration stage such that w[n]=x_(dem)[n]. The dual-tonecorrelator 34 correlates the digital signal x_(dem)[n] and outputs twomeasures U₁ and U₂, where the measure U₁ represents a desired componentwhich is a value indicative of the frequency response of x_(dem)(t) atfrequency +f_(T) Hz and the measure U₂ represents an image componentwhich is a value indicative of the frequency response of x_(dem)(t) atfrequency −f_(T) Hz. For the case that x(t)=cos(2π(f_(c)+f_(T))t),

${x_{dem}(t)} = {{\left( {{\cos\frac{\theta}{2}} - {j\;\alpha\;\sin\frac{\theta}{2}}} \right){\mathbb{e}}^{{j2\pi}\; f_{T}t}} + {\left( {{\alpha\;\cos\frac{\theta}{2}} + {j\;\sin\frac{\theta}{2}}} \right){\mathbb{e}}^{{- {j2}}\;\pi\; f_{T}t}}}$and$U_{1} = {\lambda\left( {{\cos\frac{\theta}{2}} - {j\;\alpha\;\sin\frac{\theta}{2}}} \right)}$$U_{2} = {\lambda\left( {{\alpha\;\cos\;\frac{\theta}{2}} + {j\;\sin\frac{\theta}{2}}} \right)}$where λ is a constant related to the dual-tone correlator 34.

Next, the two measures U₁ and U₂ are read by the personal computer 31,and the software stored in a personal computer 31 computes theparameters A_(p) and B_(p) required by the I/Q correction module 33according to the measures U₁ and U₂ to minimize the impacts due to theI/Q channel mismatch. In this case, we have

$\begin{matrix}{X = {{U_{1} \cdot U_{2}} = {{{\kappa\alpha} + {j\frac{\kappa\left( {1 - \alpha^{2}} \right)}{2}\sin\;\theta}} = {H + {j\; I}}}}} & (14) \\{G = {{{U_{1}}^{2} + {U_{2}}^{2}} = {\kappa\left( {1 + \alpha^{2}} \right)}}} & (15)\end{matrix}$where κ=λ², H=real(X) is the real part of X and I=imag(X) is theimaginary part of X. Since

${\kappa = {\frac{G}{\left( {1 + \alpha^{2}} \right)} > \frac{G}{2}}},$from equation (14) and (15), it can be found that

$\begin{matrix}{\kappa = {\frac{G + \sqrt{G^{2} - {4H^{2}}}}{2}.}} & (16)\end{matrix}$Consequently, the gain mismatch term is evaluated by

$\begin{matrix}{\alpha = \frac{H}{\kappa}} & (17)\end{matrix}$and we can further have

$\begin{matrix}{Q = {{\sin\;\theta} = \frac{2 \cdot I}{\kappa \cdot \left( {1 - \alpha^{2}} \right)}}} & (18) \\{P = {{\cos\;\theta} = \sqrt{1 - Q^{2}}}} & (19) \\{R = {{\cos\;\frac{\theta}{2}} = \sqrt{\frac{1 + P}{2}}}} & (20) \\{S = {{\sin\;\frac{\theta}{2}} = \frac{Q}{2 \cdot R}}} & (21)\end{matrix}$

The software stored in the personal computer 31 according to theembodiment of the present invention performs a different process fromthe prior art. Thus, the personal computer 31 implements the followingfunctions to update the coefficients A_(p) and B_(p) according to theequations (17)˜(21)

$\begin{matrix}\left\{ \begin{matrix}{A_{p} = {R + {j\;\alpha\; S}}} \\{B_{p} = {{{- \alpha}\; R} - {j\; S}}}\end{matrix} \right. & (22)\end{matrix}$

Next, the updated coefficients are fed back to the I/Q correction module33.

Additionally, the updated coefficients A_(p) and B_(p) may be normalizedso that the power of the corrected signal w[n] is the same as that ofthe digital signal x_(dem)[n].

FIG. 4 is a flowchart of a method for I/Q mismatch calibration of areceiver according to the embodiment of the present invention. Themethod is applied to a receiver having an I/Q correction module usingparameters A_(p) and B_(p). The calibration procedure of the inventionwill be specifically described in the following.

In step 41, an analog test signal x(t) is generated. The signal x(t)contains a single-tone waveform with a frequency of (f_(c)+f_(T)), wheref_(c) is the carrier frequency and f_(T) is a predetermined real number

In step 42, I/Q demodulation is applied to reduce the central frequencyof the signal x(t) by f_(c) Hz and output a demodulated signalx_(dem)(t).

In step 43, the analog signal x_(dem)(t) is converted to a digitalsignal x_(dem)[n] with sampling rate f_(s).

In step 44, the measures U₁ and U₂ of the digital signal x_(dem)[n] areobtained where U₁ and U₂ are values indicative of the frequency responseof x_(dem)(t) at frequency +f_(T) Hz and −f_(T) Hz, respectively. Themeasures U₁ and U₂ of x_(dem)(t) are obtained from the coefficients ofthe Fourier transformation of the x_(dem)[n] corresponding to thefrequency +f_(T) Hz and −f_(T) Hz. The measures U₁ and U₂ are obtainedby the dual-tone correlator 34 as shown in FIG. 3.

In step 45, the correction parameters A_(p) and B_(p) is calculated bythe personal computer for the I/Q correction module based on themeasures U₁ and U₂. The set of correction parameters (A_(p),B_(p)) isobtained by the equation (22) according to the equations (17)˜(21).

$\quad\left\{ \begin{matrix}{A_{p} = {R + {j\;\alpha\; S}}} \\{B_{p} = {{{- \alpha}\; R} - {j\; S}}}\end{matrix} \right.$

In addition, the set of correction parameters (A_(p),B_(p)) is furthernormalized by

$\begin{matrix}\left\{ {\begin{matrix}{A_{p} = {\chi\left( {R + {j\;\alpha\; S}} \right)}} \\{B_{p} = {\chi\left( {{{- \alpha}\; R} - {j\; S}} \right)}}\end{matrix}\mspace{14mu}{where}} \right. & (23) \\{\chi = \frac{1}{\left( {1 - \alpha^{2}} \right) \cdot P}} & (24)\end{matrix}$such that the power of the output signal of the I/Q correction moduleequals that of the input signal of the I/Q correction module.

The previously described method can be applied to a transceiver module,e.g., an IEEE 802.11 compliant wireless LAN transceiver module,involving I/Q demodulation. Wireless LANs based on the IEEE 802.11standard have achieved wide customer acceptance in the enterpriseenvironment. They are expected to continue to expand in popularity andbecome ubiquitous communication systems even in private and publicplaces. Prior to the circuit for I/Q mismatch calibration in the presentinvention, the basics of the IEEE 802.11 wireless LAN physical layerwill be described in the following.

Originally, the 802.11 standard was written for 1 Mb/s and 2 Mb/s datarates in the 2.4 GHz–2.5 GHz ISM band, possibly using direct sequencecode division multiplexing in combination with DBPSK and DQPSKmodulation, respectively. An eleven-chip long Barker sequence providesprocessing gain, which relaxes the SNR to below 0 dB. The channelbandwidth of 14 MHz placed anywhere in the band on a 5 MHz grid allowsnetwork configurations with 3–4 access points in close physicalproximity. The maximum RF transmitting power is 30 dBm.

The 802.11b standard option enhances the wireless LAN data rate to amaximum of 11 Mb/s by Complementary Code Keying (CCK) modulation. Whilestill using the same chip rate in order not to change the RF signalbandwidth, a much-reduced processing gain accommodates the higher datarate at the expense of approximately 10 dB higher SNR requirements.Practically, at 11 Mb/s CCK is equivalent in almost all respects toregular DQPSK.

The recent advances in RFIC and radio system technologies have providedample opportunities for the realization of miniaturized and economicallyviable wireless LAN transceivers. Typically, these blocks areimplemented using a few ICs and several hundred passives (mostly by-passcapacitors), packaged tightly into small modules such as PCMCIA cards.Usually the cost of such modules is well within the consumer electronicsmarket demands.

Focusing on the physical layer, notice that a radio chip and a base-bandchip are typically used with analog I/Q transmit and receive interfaces.The base-band chip is mostly a digital circuit, containing only dataconverters. This system partitioning minimizes the digital switchingnoise coupling into the radio sections and provides low powerchip-to-chip analog interfaces. The radio chip may be designed bydifferent technologies such as Si bipolar, SiGe BiCMOS, or recently,even in straight CMOS. Typically, a −75 dBm sensitivity is accomplishedfor about 200 mW receiver power dissipation. The radio architecture hasevolved from a conservative super-heterodyne approach to less expensivedirect down/up conversion. The efficiency of the linear power amplifieris limited by the signal peak-to-average ratio, which is moderate,allowing reasonable transmitter power dissipation, typically 500 mW.

Using the standard, one can derive the basic transceiver specifications.The following approximate calculations are not intended to give precisedesign values but rather to indicate the rough figures for 802.11a radiosystems.

The signal to noise-plus-distortion ratio (SNR) at the receiver A/Doutput is the primary overall design requirement. Starting with the −174dBm/Hz background thermal noise and adding 73 dB corresponding to the 20MHz channel bandwidth we obtain −101 dBm for the antenna noise.Subtracting this number from the required −65 dBm receiver sensitivity(minimum antenna signal), we calculate an input SNR of 36 dB. Since thestandard assumes a 15 dB noise figure (NF) receiver, everything elsebeing ideal, 21 dB SNR results at the output of the receiver A/Dconverter. This is a static channel calculation, assuming no fading andnot taking into account the SNR loss in the base-band processing due tomany error sources.

If fading is present, the previous calculation is amended by about a 5dB “channel correction factor”, as it can be simulated for a 54 Mb/swith 50 ns RMS delay spread. The required SNR at the output of the A/Dconverter jumps to approximately 26 dB. Furthermore, transmitter andreceiver practical errors are usually responsible for at least 3–4 dBperformance deterioration so a final 30 dB SNR is estimated. Referringthis number back to the original SNR calculation and assuming the same−65 dBm sensitivity, we see that a practical receiver will have a NFless than 7 dB. Notice that the only ways the design methodology canmake a difference in the transceiver performance are by minimizing thereceiver NF and the various practical errors mentioned previously. Forthis reason it is instructive to identify these errors and the circuitblocks where they are produced.

The “receiver thermal noise” is independent of the signal and is givenby the NF. The “receiver implementation noise” is signal dependent andis produced by many non-idealities such as local oscillator noise,non-linearity in receiver chain, I/Q imbalances (mismatch), DC offsets,A/D converter quantization noise, residual adjacent channels or blockersdue to insufficient filtering, etc. We see that a large number ofnegative factors produce errors, which can easily add up to many SNR dBlosses.

In conclusion, the present invention provides a new method and apparatusfor receiver I/Q mismatch calibration, especially suitable for an IEEE802.11 compliant WLAN transceiver module. The compensation of the I/Qmismatch is achieved by an I/Q correction module posterior to the I/Qdemodulator.

The foregoing description of the preferred embodiments of this inventionhas been presented for purposes of illustration and description. Obviousmodifications or variations are possible in light of the above teaching.The embodiments were chosen and described to provide the bestillustration of the principles of this invention and its practicalapplication to thereby enable those skilled in the art to utilize theinvention in various embodiments and with various modifications as aresuited to the particular use contemplated. All such modifications andvariations are within the scope of the present invention as determinedby the appended claims when interpreted in accordance with the breadthto which they are fairly, legally, and equitably entitled.

1. A method for I/Q mismatch calibration of a receiver having an I/Qcorrection module which performsx_(o)[n]=A_(p)·x_(i)[n]+B_(p)·x*_(i)*[n] where x_(i)[n] and x_(o)[n]respectively represent the input and output signal of the I/Q correctionmodule, the superscript * refers to a complex conjugate, and A_(p) andB_(p) are correction parameters, comprising the following steps:generating a test signal x(t) containing a single tone waveform withfrequency of (f_(c)+f_(T)) Hz, where f_(c) and f_(T) are real numbers;applying I/Q demodulation to reduce the central frequency of the testsignal x(t) by f_(c) Hz and output a demodulated signal x_(dem)(t);converting the demodulated signal x_(dem)(t) to a digital signalx_(dem)[n]; obtaining measures U₁ and U₂ of the digital signalx_(dem)[b] where U₁ and U₂ are values indicative of the frequencyresponse of x_(dem)(t) at frequency +f_(T) Hz and −f_(T) Hz,respectively; and calculating the set of the correction parameters A_(p)and B_(p) for the I/Q correction module based on the measures U₁ and U₂.2. The method for I/Q mismatch calibration of a receiver as claimed inclaim 1, the measure U₁ and U₂ are obtained from the coefficients of theFourier transformation of the x_(dem)[n] corresponding to the frequency+f_(T) Hz and −f_(T) Hz.
 3. The method for I/Q mismatch calibration of areceiver as claimed in claim 1, wherein the test signalx(t)=cos(2π(f_(c)+f_(T))).
 4. The method for I/Q mismatch calibration ofa receiver as claimed in claim 1, wherein the set of correctionparameters (A_(p),B_(p)) are obtained by $\quad\left\{ \begin{matrix}{A_{p} = {R + {j\;\alpha\; S}}} \\{B_{p} = {{{- \alpha}\; R} - {j\; S}}}\end{matrix} \right.$ where α, R, and S are obtained based on U₁ and U₂.5. The method for I/Q mismatch calibration of a receiver as claimed inclaim 4, wherein α, R, and S are obtained based onH=real(U ₁ ·U ₂),I=imag(U ₁ ·U ₂), andG=|U ₁|² +|U ₂|².
 6. The method for I/Q mismatch calibration of areceiver as claimed in claim 4.1, wherein α, R, and S are obtained by${\alpha = \frac{H}{\kappa}},\mspace{14mu}{{{where}\mspace{14mu}\kappa} = \frac{G + \sqrt{G^{2} - {4H^{2}}}}{2}},\mspace{14mu}{{{and}\mspace{14mu} R} = \sqrt{\frac{1 + P}{2}}},\mspace{14mu}{S = \sqrt{\frac{Q}{{2 \cdot \sqrt{\frac{1 + P}{2}}}\;}}},\mspace{14mu}{{{where}\mspace{14mu} Q} = \frac{2 \cdot I}{\kappa \cdot \left( {1 - \alpha^{2}} \right)}},\mspace{14mu}{P = {\sqrt{1 - \left( \frac{2 \cdot I}{\kappa \cdot \left( {1 - \alpha^{2}} \right)} \right)^{2}}.}}$7. The method for I/Q mismatch calibration of a receiver as claimed inclaim 4, wherein the set of correction parameters (A_(p), B_(p)) isfurther normalized such that the power of the output signal of the I/Qcorrection module equals to that of the input signal of the I/Qcorrection module.
 8. An apparatus for I/Q mismatch calibration of areceiver having an I/Q correction module which performsx_(o)[n]=A_(p)·x_(i)[n]+B_(p)·x*_(i)[n] where x_(i)[n] and x_(o)[n]respectively represent the input and output signal of the I/Q correctionmodule, the superscript * refers to a complex conjugate, and A_(p) andB_(p) are correction parameters, comprising: a signal generator forgenerating a test signal x(t) which contains a single tone waveform withfrequency of (f_(c)+f_(T)) Hz, where f_(c) and f_(T) are real numbers; ademodulator for applying I/Q demodulation to reduce the centralfrequency of the test signal x(t) by f_(c) Hz and outputting ademodulated signal x_(dem)(t); A/D converters for converting thedemodulated signal x_(dem)(t) to a digital signal x_(dem)[n]; adual-tone correlator for obtaining measures U₁ and U₂ of the digitalsignal x_(dem)[n] output from the I/Q correction module where U₁ and U₂are values indicative of the frequency response of x_(dem)(t) atfrequency +f_(T) Hz and −f_(T) Hz, respectively; and a processor forobtaining the set of the correction parameters A_(p) and B_(p) accordingto the measures U₁ and U₂.
 9. The apparatus for I/Q mismatch calibrationof a receiver as claimed in claim 8, the measure U₁ and U₂ are obtainedfrom the coefficients of the Fourier transformation of the x_(dem)[n]corresponding to the frequency +f_(T) Hz and −f_(T) Hz.
 10. Theapparatus for I/Q mismatch calibration of a receiver as claimed in claim8, wherein the test signal x(t)=cos(2π(f_(c)+f_(T))).
 11. The apparatusfor I/Q mismatch calibration of a receiver as claimed in claim 8,wherein the set of correction parameters (A_(p), B_(p)) are obtained by$\quad\left\{ \begin{matrix}{A_{p} = {R + {j\;\alpha\; S}}} \\{B_{p} = {{{- \alpha}\; R} - {j\; S}}}\end{matrix} \right.$ where α, R, and S are obtained based on U₁ and U₂.12. The apparatus for I/Q mismatch calibration of a receiver as claimedin claim 11, wherein α, R, and S are obtained based onH=real(U ₁ ·U ₂),I=imag(U ₁ ·U ₂), andG=|U ₁|² +|U ₂|².
 13. The apparatus for I/Q mismatch calibration of areceiver as claimed in claim 12, wherein α, R, and S are obtained by${\alpha = \frac{H}{\kappa}},\mspace{14mu}{{{where}\mspace{14mu}\kappa} = \frac{G + \sqrt{G^{2} - {4H^{2}}}}{2}},\mspace{14mu}{{{and}\mspace{14mu} R} = \sqrt{\frac{1 + P}{2}}},\mspace{14mu}{S = \sqrt{\frac{Q}{{2 \cdot \sqrt{\frac{1 + P}{2}}}\;}}},\mspace{14mu}{{{where}\mspace{14mu} Q} = \frac{2 \cdot I}{\kappa \cdot \left( {1 - \alpha^{2}} \right)}},\mspace{14mu}{P = {\sqrt{1 - \left( \frac{2 \cdot I}{\kappa \cdot \left( {1 - \alpha^{2}} \right)} \right)^{2}}.}}$14. The apparatus for I/Q mismatch calibration of a receiver as claimedin claim 11, wherein the set of correction parameters (A_(p), B_(p)) isfurther normalized such that the power of the output signal of the I/Qcorrection module equals to that of the input signal of the I/Qcorrection module.